Three-dimensional bin packing problem with variable bin height

This paper studies a variant of the three-dimensional bin packing problem (3D-BPP), where the bin height can be adjusted to the cartons it packs. The bins and cartons to be packed are assumed rectangular in shape. The cartons are allowed to be rotated into any one of the six positions that keep the carton edges parallel to the bin edges. This greatly increases the difficulty of finding a good solution since the search space expands significantly comparing to the 3D-BPP where the cartons have fixed orientations. A mathematical (mixed integer programming) approach is modified based on [Chen, C. S., Lee, S. M., Shen, Q. S., 1995. An analytical model for the container loading problem. European Journal of Operational Research 80 (1), 68–76] and numerical experiments indicate that the mathematical approach is not suitable for the variable bin height 3D-BPP. A special bin packing algorithm based on packing index is designed to utilize the special problem feature and is used as a building block for a genetic algorithm designed for the 3D-BPP. The paper also investigates the situation where more than one type of bin are used and provides a heuristic for packing a batch of cartons using the genetic algorithm. Numerical experiments show that our proposed method yields quick and satisfactory results when benchmarked against the actual packing practice and the MIP model with the latest version of CPLEX.     

On solving the chaotic Chen system: a new time marching design for the variational iteration method using Adomian’s polynomial

This paper centres on the effectiveness of the variational iteration method and its modifications for numerically solving the chaotic Chen system, which is a three-dimensional system of ODEs with quadratic nonlinearities. This research implements the multistage variational iteration method with an emphasis on the new multistage hybrid of variational iteration method with Adomian polynomials. Numerical comparisons are made between the multistage variational iteration method, the multistage variational iteration method using the Adomian’s polynomials and the classic fourth-order Runge-Kutta method. Our work shows that the new multistage hybrid provides good accuracy and efficiency with a performance that surpasses that of the multistage variational iteration method.     

A predictive gradient strategy for multiobjective evolutionary algorithms in a fast changing environment

An essential feature of a dynamic multiobjective evolutionary algorithm (MOEA) is to converge quickly to the Pareto-optimal Set before it changes. In cases where the behavior of the dynamic problem follows a certain trend, convergence can be accelerated by anticipating the characteristics of future changes in the problem. A prediction model is usually used to exploit past information and estimate the location of the new Pareto-optimal Set. In this work, we propose the novel approach of tracking and predicting the changes in the location of the Pareto Set in order to minimize the effects of a landscape change. The predicted direction and magnitude of the next change, known as the predictive gradient, is estimated based on the history of previously discovered solutions using a weighted average approach. Solutions updated with the predictive gradient will remain in the vicinity of the new Pareto-optimal Set and help the rest of the population to converge. The prediction strategy is simple to implement, making it suitable for fast-changing problems. In addition, a new memory technique is introduced to exploit any periodicity in the dynamic problem. The memory technique selects only the more promising stored solutions for retrieval in order to reduce the number of evaluations used. Both techniques are incorporated into a variant of the multi-objective evolutionary gradient search (MO-EGS) and two other MOEAs for dynamic optimization and results indicate that they are effective at improving performance on several dynamic multiobjective test problems.     

Synthesis and characterization of high refractive index polyimides derived from 2,5‐Bis(4‐Aminophenylenesulfanyl)‐3,4‐Ethylenedithiothiophene and aromatic dianhydrides

The authors describe the synthesis and characterization of the polyimide (PI) series containing a 2,5‐bis(4‐aminophenylenesulfanyl)‐3,4‐ethylenedithiothiophene (APSEDTT) moiety in their main chain. The APSEDTT monomer with high sulfur content was prepared and polymerized with several aromatic dianhydrides such as 4,4′‐[p‐thio bis(phenylenesulfanyl)]diphthalic anhydride (3SDEA), 4,4′‐biphthalic anhydride (BPDA), and 4,4′‐oxydiphthalic anhydride (ODPA) by the traditional two‐step polycondensation procedure. All PIs exhibited high transparency, higher than 75% at 550 nm for a thickness of about 20 μm and good thermal properties such as thermal decomposition temperatures (T_10%) in the range of 409–521 °C. In addition, the PIs have extraordinarily excellent optical properties in refractive index and birefringence as originally designed. In particular, the PI derived from APSEDTT and 3SDEA showed a high refractive index (1.7586), and a low birefringence (0.0087) because of their very high sulfur content (27.7%). © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 944–950     

Poly(dicyclopentadiene)‐montmorillonite nanocomposite formation via simultaneous intergallery‐surface initiation and chain crosslinking using ROMP

Exfoliated poly(dicyclopentadiene) (pDCPD)—montmorillonite (MMT) nanocomposites were synthesized via intergallery‐surface‐initiated ring opening metathesis polymerization (ROMP). This is the first example of in situ polymerization of pDCPD from clay intergallery surfaces using ROMP. Grubbs catalyst was immobilized on the surface of MMT clay modified with vinylbenzyl dimethyloctadecyl ammonium chloride (VOAC), and DCPD polymerized from the clay surface while simultaneously crosslinking to form a thermoset nanocomposite in a one‐pot reaction. X‐ray diffraction and transmission electron microscopy analysis indicated that the resultant nanocomposites exhibited exfoliated morphologies with heterogeneous clay platelet distribution. Conventional bulk‐initiated nanocomposites containing VOAC modified MMT were also synthesized as a comparison, and these resulted in nanocomposites with intercalated morphologies. The differences between the morphologies demonstrated that growing polymer chains from the initiator sites on the intergallery surface of the clay platelets pushed the platelets apart during the polymerization of the intergallery‐surface‐initiated nanocomposites, aiding in the exfoliation process. Compression testing indicated that the intergallery‐surface‐initiated nanocomposites led to improvements of up to 50% in the compressive Young's Modulus, while the bulk‐initiated nanocomposites at the same clay loadings did not exhibit improved properties. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Uncertainty Principles in Hilbert Spaces

In this article we provide several generalizations of inequalities bounding the commutator of two linear operators acting on a Hilbert space which relate to the Heisenberg uncertainty principle and time/frequency analysis of periodic functions. We develop conditions that ensure these inequalities are sharp and apply our results to concrete examples of importance in the literature.     

Di­chloro­bis­(tri­methyl­ene­thio­urea‐κS)antimony(III) chloride

In the title compound, [SbCl₂(C₄H₈N₂S)₂]Cl, the coordination around the Sb atom can be described as distorted pseudo‐octahedral. Both rings of the tri­methyl­ene­thio­urea ligands [alternatively 3,4,5,6‐tetrahydropyrimidine‐2(1H)‐thione] adopt an envel­ope conformation. The mol­ecules are connected into dimers in the ab plane by two intermolecular hydrogen bonds. The dimers are arranged into infinite one‐dimensional chains along the a axis as a result of the Cl^? ions forming intermolecular hydrogen bonds with three NH groups.     

An Adjustable Pure Dispersion Slope Compensating-Module without Center Wavelength Shift Based on Strain-Chirped Fiber Bragg Gratings

We demonstrate an adjustable pure dispersion slope compensating-module based on strain-chirped fiber Bragg gratings.The center wavelength of the module is preserved while the pure dispersion slope is tuned.     

Specific interactions and phase behavior of ternary poly(2‐vinylpyridine)/poly(N‐vinyl‐2‐pyrrolidone)/bisphenol A blends

Hydrogen‐bonding interactions between bisphenol A (BPA) and two proton‐accepting polymers, poly(2‐vinylpyridine) (P2VPy) and poly(N‐vinyl‐2‐pyrrolidone) (PVP), were examined by Fourier transform infrared (FTIR) spectroscopy and differential scanning calorimetry (DSC). The Flory–Huggins interaction‐energy densities of BPA/P2VPy and BPA/PVP blends were determined by the melting point depression method. The interaction parameters for both BPA/P2VPy and BPA/PVP blend systems were negative, demonstrating the miscibility of BPA with P2VPy as well as PVP. The miscibility of ternary BPA/P2VPy/PVP blends was examined by DSC, optical observation, and solid‐state nuclear magnetic resonance spectroscopy. The experimental phase behavior of the ternary blend system agreed with the spinodal phase‐separation boundary calculated using the determined interaction‐energy densities. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1125–1134, 2002